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Matrix Compression using the Nystrom Method Arik Nemtsov1

Summary: Matrix Compression using the Nystr¨om Method
Arik Nemtsov1
Amir Averbuch1
Alon Schclar2
School of Computer Science
Tel Aviv University, Tel Aviv 69978
School of Computer Science
The Academic College of Tel Aviv-Yaffo ,Tel Aviv, 61083
The Nystr¨om method is routinely used for out-of-sample extension of kernel ma-
trices. We describe how this method can be applied to find the singular value de-
composition (SVD) of general matrices and the eigenvalue decomposition (EVD) of
square matrices. We take as an input a matrix M Rm×n, a user defined integer
s min(m, n) and AM Rs×s, a matrix sampled from columns and rows of M. These
are used to construct an approximate rank-s SVD of M in O s2 (m + n) operations.
If M is square, the rank-s EVD can be similarly constructed in O s2n operations. In
this sense, AM is a compressed version of M.
We discuss theoretical considerations for the choice of AM and how it relates to the


Source: Averbuch, Amir - School of Computer Science, Tel Aviv University


Collections: Computer Technologies and Information Sciences